Comparative Study between Kleinberg Algorithm and Biased Selection Algorithm for Construction of Small World Networks

Abstract

Actually Small-World Networks is a very important topic, it is present in a lot of applications in our environment. A target of many algorithms is to establish methods to get that any node in a graph can establish a direct connection with a randomly “long-range neighbor”. This work is comparative study between two algorithms that get this target (Kleinberg and Biased Selection), I demonstrate by my experiments that both get the Kleinberg’s distribution. I conclude that the Kleinberg’s algorithm distribution maintains a probability directly proportional to Euclidian distance, and Biased Selection, although also maintains a probability directly proportional to Euclidian distance, allows that a node can get a farther node as “long-range neighbor” more frequently.